Joukowski mapping

[matt07]

Hi, Im currently looking at Joukowski mapping but having difficulty answering one of the questions. Any assistance would be highly appreciated.

1. An ellipse of length to beam ratio λ is set with its major axis parallel to a uniform stream of speed U. Show that the maximum flow speed at any point on the surface of the ellipse is U (1 + λ1 ). At what point does this maximum velocity occur? How close to the ellipse can one approach along centreline before the disturbance of the ellipse is less than 1% of the free stream speed for the case λ = 4.

Thanks

Matt

 

[Deleted member 4993]

Hi, Im currently looking at Joukowski mapping but having difficulty answering one of the questions. Any assistance would be highly appreciated.

1. An ellipse of length to beam ratio λ is set with its major axis parallel to a uniform stream of speed U. Show that the maximum flow speed at any point on the surface of the ellipse is U (1 + λ1 ). At what point does this maximum velocity occur? How close to the ellipse can one approach along centreline before the disturbance of the ellipse is less than 1% of the free stream speed for the case λ = 4.

Thanks

Matt

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

https://www.freemathhelp.com/forum/threads/read-before-posting.109846/#post-486520

Please share your work/thoughts about this assignment.

 

[matt07]

Hi, my apologies.

I see that on the major axis it maps to an ellipse of a + 1/a.

The flow around an ellipse is - w=U (z+ a^2 / z)

z is a circle of radius a.

I am just not sure how they get to that maximum flow. I am quite confused by the process.

Thanks

Matt